Complete the square to solve for $x$. $x^{2}+17x+70 = 0$
Explanation: Move the constant term to the right side of the equation. $x^2 + 17x = -70$ We complete the square by taking half of the coefficient of our $x$ term, squaring it, and adding it to both sides of the equation. The coefficient of our $x$ term is $17$ , so half of it would be $\dfrac{17}{2}$ , and squaring it gives us ${\dfrac{289}{4}}$ $x^2 + 17x { + \dfrac{289}{4}} = -70 { + \dfrac{289}{4}}$ We can now rewrite the left side of the equation as a squared term. $( x + \dfrac{17}{2} )^2 = \dfrac{9}{4}$ Take the square root of both sides. $x + \dfrac{17}{2} = \pm\dfrac{3}{2}$ Isolate $x$ to find the solution(s). $x = -\dfrac{17}{2}\pm\dfrac{3}{2}$ The solutions are: $x = -7 \text{ or } x = -10$ We already found the completed square: $( x + \dfrac{17}{2} )^2 = \dfrac{9}{4}$